What is the integral of x^9ln(2x^5) ?

The integral of x^9ln(2x^5) is 1/10 x^{10}(ln(2)+5ln(x))-(x^{10})/(20)+C

Popular >

integral of x^9ln(2x^5)

\int x^{9} ln (2 x^{5}) d x

\frac{1}{10} x^{10} (ln (2) + 5 ln (x)) - \frac{x ^{10}}{20} + C

Solution steps

\int x^{9} ln (2 x^{5}) d x

Apply Integration By Parts

: \frac{1}{10} x^{10} ln (2 x^{5}) - \int \frac{x ^{9}}{2} d x

= \frac{1}{10} x^{10} ln (2 x^{5}) - \int \frac{x ^{9}}{2} d x

\int \frac{x ^{9}}{2} d x = \frac{x ^{10}}{20}

= \frac{1}{10} x^{10} ln (2 x^{5}) - \frac{x ^{10}}{20}

Simplify

ln (2 x^{5}) : 5 ln (x) + ln (2)

= \frac{1}{10} x^{10} (ln (2) + 5 ln (x)) - \frac{x ^{10}}{20}

Add a constant to the solution

= \frac{1}{10} x^{10} (ln (2) + 5 ln (x)) - \frac{x ^{10}}{20} + C

\int (\frac{1}{( 5 x - 3 ) ( 3 - 4 x )}) d x

\int \frac{arctan ( 2 t )}{1 + 4 t ^{2}} d t

\int sin^{3} (\frac{2 x}{3}) d x

\int \frac{x + 2}{( x ^{2} + 4 x - 1 ) ^{2}} d x

\int \frac{e ^{3 x}}{4 + e ^{6 x}} d x

What is the integral of x^9ln(2x^5) ?
The integral of x^9ln(2x^5) is 1/10 x^{10}(ln(2)+5ln(x))-(x^{10})/(20)+C